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Ernie Accorsi used to talk about how the weeks leading up to the NFL draft were the most important of the year in terms of molding his team. At least the retired New York Giants general manager had the luxury of making plans to fill any leftover holes with free agents.

Jerry Reese and the rest of the NFL’s general managers aren’t as fortunate this year. The recently lifted (but soon to be appealed) lockout has prevented teams from contacting players – even their own – and the lack of a labor agreement means teams have no way to estimate this year’s salary cap (if there is one) or how many years a veteran must have played before gaining unrestricted free agency.

So the biggest question facing the Giants, a team close enough to believe it may contend this season, is how much additional weight must be placed on the organization’s needs rather than the prospects’ grades during the draft. Reese always has said he attempts to balance both factors, however, he’s never been faced with cap and free agent uncertainty as part of the process.

For the record, three of Reese’s first-round picks since he became the Giants’ GM matched significant need with value: CB Aaron Ross (2007), S Kenny Phillips (2008) and WR Hakeem Nicks (2009). Reese allowed value to steer his decision when he nabbed DE Jason Pierre-Paul last year, although the rookie saw his role increase once veteran Mathias Kiwanuka left the lineup with a serious neck injury and, thus, created a significant need.

The most obvious commodity the team could use this year is an impact linebacker, but this is a very weak draft for linebackers – OLB Von Miller will be taken very high and has no chance to fall near the Giants at No. 19.

Before we run down a list of good fits for the Giants, remember that they have several key starters who could become unrestricted free agents once the CBA situation is settled: TE Kevin Boss, RB Ahmad Bradshaw, DT Barry Cofield, Mathias Kiwanuka and Steve Smith and it’s likely they’d be interested in re-signing veteran free agent S Deon Grant, who already qualifies as unrestricted.

Here are the players (in alphabetical order) who the Giants likely have on their radar if they stay at No. 19:

GABE CARIMI, OT, WISCONSIN

Why this pick makes sense:The Giants’ biggest need on offense is along their line, given its age, injuries and contract status. Veterans C Shaun O’Hara (ankle, foot) and LG/C Rich Seubert (knee) and young backup C Adam Koets (knee) are coming off surgeries. Swing lineman Shawn Andrews remains a mystery because of chronic back issues and he’s due to earn a $3.5M roster bonus to go with a $3M salary – which makes him too expensive risk to keep at those numbers. Reese may be satisfied with versatile backups Kevin Boothe and Mitch Pietrus, but it would be unwise to ask either to provide playoff-caliber football as a starter. Carimi is a power blocker who may be the perfect right tackle, but scouts also have discussed him as a left tackle and even as a road-grading guard. In other words, he’s “versatile” – music to the ears of highly respected Giants offensive line coach Pat Flaherty.

Why they might pass: Carimi may have the most experience and the most power of the top prospects at left tackle, but his technique needs to be refined if he’s going to stay there in the NFL – as he says insists he will. Is that attitude a positive or might it turn into a negative if he continues to believe he’s a left tackle while the team tells him he’s got to settle in and learn one or more positions?

ANTHONY CASTONZO, OT, BOSTON COLLEGE

Why this pick makes sense: See Carimi for the Giants’ perspective on taking an offensive lineman. Castonzo is regarded at a pure talent with a high football acumen, which should translate into a rock-solid tackle – right or left – for many years to come. If they make this pick, it likely is being done with the intention of forcing the versatile David Diehl to become the starting left guard.

Why they might pass: Simply put, if the hype about Castonzo being a legit foundation-type tackle, he’ll be gone long before the Giants pick, anyway. Should he drop to No. 19, there are a few warning signs to consider – he’s not as forceful in the running game as the Giants would like, perhaps because he needs to improve his size and lower-body strength. He oversets in his stance to play the edge, stands too upright and has appeared disinterested, at times.

MARK INGRAM, RB, ALABAMA

Why this pick makes sense: Ingram, who often has been compared to Emmitt Smith, is the most talented running back in this year’s draft and easily would be a Top 10 pick if it were not for his injured knee. Ingram, the son of former Giants WR Mark Ingram, also could provide the Giants with their most dangerous check-down target out of the backfield since Tiki Barber. A bigger question is: How do you NOT consider Ingram if he falls to No. 19? This could be a repeat of last spring, when the Giants kept C.J. Spiller on their final want list at No. 15, just in case the Top 10 talent fell to them – but he did not. Brandon Jacobs sounds as though he may be willing to renegotiate down from his $4.65M base for 2011, although those talks could get sticky while the status of free agent Ahmad Bradshaw (and his balky ankles/feet) is subject to the rules of the new CBA.

Why they would pass: Jacobs proved last season (career-high 5.6 avg, 9 rushing TDs) that he could be effective over 16 games even though coach Tom Coughlin admitted the team took away too much of Jacobs’ workload. Bradshaw is only 25 and coming off a career-high 1,235 rushing yards and the often-injured Danny Ware was re-signed to get a final shot at staying healthy enough to become the third member of the backfield rotation. In addition, there are whispers around the NFL that Ingram is dealing with an arthritic knee that would limit his long-term future as a pro.

COREY LIUGET, DT, ILLINOIS

Why this pick makes sense: Starting DT Barry Cofield, whose contract has run out, is one of those players who won’t learn of his free agent status until after the labor situation is resolved. However, he’s said he’d rather be traded than play under another one-year contract with the Giants. With similar circumstances last spring, they agreed to deal him to the Saints, but New Orleans was unable to reach a new deal with Cofield, who wound up rebounding with a terrific season in New York. Reese has high hopes for second-year DT Linval Joseph, but he’s more of a space-eating tackle. Illinois coach Ron Zook has compared Liuget to former Pro Bowl lineman La’Roi Glover. Liuget is suited to be a “three-technique” tackle in a four-man line, allowing him to use his emphasize his quickness and penetration rather than asking him to hold up blockers at the line of scrimmage. In effect, he would replace Cofield.

Why they might pass: The Giants may be confident they will retain Cofield. They’ve also got Chris Canty and Joseph while veteran Rocky Bernard might be able to stick around for one more season with a strong camp. Keep in mind, the Giants often slide DE Justin Tuck and/or DE Jason Pierre-Paul inside as part of their sub packages, so they are in not desperate for a full-time player on the inside.

MIKE POUNCEY, G/C, FLORIDA

Why this pick makes sense: See Carimi for the Giants’ perspective on taking an offensive lineman. Pouncey has proven to be versatile in a pro-style offense and comes with an NFL pedigree, thanks to his Pro Bowl brother, Maurkice, who starts for the Steelers.

Why they might pass: Pouncey needs to improve his consistency, specifically getting physical as a drive blocker and he has shorter arms than some would like to see in a center. We may see as many as nine centers and/or guards selected over the first two days of this draft and highly respected offensive line coach Pat Flaherty has proven he can develop talent, so the Giants may prefer to wait until the second round to grab a lineman (remember William Beatty was a second-round pick in 2009).

NATE SOLDER, OT, COLORADO

Why this pick makes sense: See Carimi for the Giants’ perspective on taking an offensive lineman. Some scouts project Solder to wind up being the best left tackle in this draft. A converted tight end with a strong work ethic, many suggest he simply needs experience, additional power and technique refinement to become a dominant force. Remember, Reese has shown a preference for athleticism and is known to prefer that his linemen have long arms – remember how he selected DL Jason Pierre-Paul last season.

Why they might pass: Some scouts suggest that it’s too easy to be impressed with Solder’s athleticism and he’ll fall short of his potential in the pros. He’s also going to need time to develop – something the Giants may not feel they have in light of their line’s current status.

** Here are several other prospects who could intrigue the Giants after the first round:

OLB Bruce Carter (North Carolina) would have been no worse than a Top 15 pick if he did not suffer a torn ACL last season. He has all the traits to be the impact player the Giants need, although there’s some question as to whether he’ll be healthy enough to play by opening day. It’s expected the injury will slide him into the early second round – so the may have to trade up from No. 52 to get him.

Other second-round possibilities include oft-injured CB Ras-I Dowling (Virginia) , who has all of the tools and been heavily scouted by the Giants; DT Jurrell Casey (Southern Cal), an intense, physical, athletic big man; C/G Stefan Wisniewski (Penn State), a heady player whose uncle, Steve, was an eight-time Pro Bowl pick with the Raiders; and G/CRodney Hudson (Florida State), a four-year starter who has got a great motor.

In the third round, you should watch for speedy CBs Davon House (New Mexico State and heavily scouted by the Giants), Shareece Wright (Southern Cal),who overcame a neck injury in college and Chimidi Chekwa (Ohio State), coming off a wrist injury; TE Luke Stocker (Tennessee) , a steady all-around talent and good in-line blocker; and OLB Dontay Moch (Nevada), who played DE in college and is better suited for a 3-4 scheme but owns explosive pass-rushing skills.

Draft schedule: First round (with a maximum of 10 minutes between each pick) begins Thursday at 8 p.m. The second round (seven minutes) and third round (five minutes) will be Friday, starting at 6 p.m. Rounds four through seven (five minutes) begin Saturday at noon.